With respect to STG, the calculation of spatial modes required for synthetic turbulence has been validated and the perturbations are calculated ( v’ in the Shur et al.1). Following figures are attached:
Blue portion in figure(b) is the wave numbers (with corresponding energy) that are used in the calculation of modes. Some points regarding the calculation:
- There are two cut-off for the energy spectrum modes defined through empirical functions
corresponds to Kolmogorov length scale. Shur et al. have defined the Kolmogorov length scale to be
- For the SA model, turbulence dissipation rate ε does not exist. In the current implementation, Kolmogorov length scale is based on minimum wall normal spacing. Other definition of Kolmogorov Scale, that was tested
- where S is a strain ( also used in the definition of
). This definition results in values of Kolmogorov scale that does not lead to the correct cut-off in the modes.
- The wave numbers are defined as
- Shur et al. used
=0.01 and obtained N = 405 by satisfying inequality
- In the current implementation,
= 0.03, and N is obtained to be 500.
To obtain velocity fluctuation that goes into the solution, the ‘modes’ vector is multiplied with Reynolds stress tensor. I am currently working on obtaining Reynolds stress tensor correctly from the existing RANS solution.
- In the current implementation, the modes computation is done on CPU since it is a one-time calculation.
- Velocity fluctuation calculation is done on GPU since it needs to be calculated every time step for external flows.
- For channel flow, we do not need to calculate time-wise velocity fluctuations as we will be recirculating the initially calculated fluctuations.